“You walk down the street,” Mr. Trump said in his first debate with Hillary Clinton, “you get shot.”

It often sounds as if he is describing the Bronx in the 1970s, and not American cities like New York and Washington, D.C., that today surround his own real estate projects.

But that’s the power of this perception. The phrase “inner city” is often used to suggest that the historical image and the modern place are one and the same — or even that the “inner city” is still a meaningfully identifiable place at all, with clearly implied demographics (black, poor) and connotations (violence, decay). It still invokes the particular context when the phrase became popular in the 1960s and ’70s.